Problem Based on ages

Problem Based on ages

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  1. The ages of Samir and Saurabh are in the ratio of 8 : 15 respectively . After 9 years the ratio of their ages will be 11 : 18. What is the difference between their ages in years?








  1. View Hint View Answer Discuss in Forum

    Let the present ages of Samir and Saurabh are 8a and 15a years respectively.

    Correct Option: B

    Let the present ages of Samir and Saurabh are 8a and 15a years respectively ; .
    After 9 years the ages of Samir and Saurabh will be 8a + 9 and 15a + 9.
    According to question,
    After 9 years the ratio of their ages will be 11 : 18, then
    (8a + 9)/ = 11/18
    ⇒ (8x + 9) x 18 = 11 x (15a + 9)
    ⇒ 144a + 162 = 165a + 99
    ⇒ 21a = 63
    ∴ a = 3
    Hence, difference of their ages = 15a - 8a = 7a = 7 x 3 = 21 years

  1. The difference between the ages of a boss and his subordinate is 16 years. Four years ago, the respective ratio of the ages of the boss and subordinate was 11 : 7. The present age of the subordinate is:








  1. View Hint View Answer Discuss in Forum

    Let us assume the present age of the subordinate is P then her Boss age will be (P + 16).

    Correct Option: B

    Let us assume the present age of the subordinate is P then her subordinate age will be (P + 16).
    According to Question,
    Four years ago, the respective ratio of the ages of the boss and subordinate was 11 : 7.
    (P +16 - 4 )/ (P - 4) = 11/7
    ⇒ 7 x (P +16 - 4 ) = 11 x (P - 4)
    ⇒ 7 x (P +12 ) = 11 x (P - 4)
    ⇒ 7P + 84 = 11P - 44
    ⇒ 4P = 128
    ∴ P = 32 years

  1. The average age of a cricket team is 27 years. Two players with 24 and 27 years of age are replaced by new players of 23 and 28 years of age. What is the average age of the team now?








  1. View Hint View Answer Discuss in Forum

    According to question ,
    The average age of a cricket team = 27 years
    Age of two old players = 24 + 27 = 51
    Age of two new players = 23 + 28 = 51
    ∴ New average age of a cricket team = 27 + ( Age of two old players ) - ( Age of two new players )
    New average age of a cricket team = 27 + ( 51 ) - ( 51 ) = 27 years

    Correct Option: A

    According to question ,
    The average age of a cricket team = 27 years
    Age of two old players = 24 + 27 = 51
    Age of two new players = 23 + 28 = 51
    ∴ New average age of a cricket team = 27 + ( Age of two old players ) - ( Age of two new players )
    New average age of a cricket team = 27 + ( 51 ) - ( 51 ) = 27 years
    In other words ,The total age of the two players which were replaced is the same as that of the total age of two players which replaced them. Therefore, the new average will remain unchanged.

  1. The age of X is 2/3 rd that of Y. After 6 years X will be 46 years old.
    What is the present age of Y ?








  1. View Hint View Answer Discuss in Forum

    According to question , we have

    Age of X =
    2
    		Age of Y
    3

    ∴ Age of Y =
    3
    		Age of X .......( 1 )
    2

    Correct Option: C

    According to question , we have

    Age of X =
    2
    		Age of Y
    3

    ∴ Age of Y =
    3
    		Age of X .......( 1 )
    2

    After 6 years , Age of X = 46 years
    ∴ Present age of X = 46 – 6 = 40 years
    From eq. ( 1 ) , we get
    Now, Present age of Y =
    3
    		 x 40 = 60 years
    2

  1. A, B, C, D, are four friends. Average age of A and C is 35 years and that of B, and D is 40 years. Average age of B, C and D is 40 years. The sum of the ages of A and D is equal to that of B and C. Find out the ages (in years) of A, B, C and D.








  1. View Hint View Answer Discuss in Forum

    Given :- Average age of A and C = 35 years
    ⇒ A + C = 70 years ......... ( ⅰ )
    Average age of B, and D = 40 years.
    ⇒ B + D = 80 years ......... ( ⅱ )
    and Average age of B, C and D = 40 years.
    ⇒ B + C + D = 120 years ......... ( ⅲ )
    With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get
    ∴ age of C = 40 years and age of A = 30 years

    Correct Option: C

    Given :- Average age of A and C = 35 years
    ⇒ A + C = 70 years ......... ( ⅰ )
    Average age of B, and D = 40 years.
    ⇒ B + D = 80 years ......... ( ⅱ )
    and Average age of B, C and D = 40 years.
    ⇒ B + C + D = 120 years ......... ( ⅲ )
    With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get
    ∴ age of C = 40 years and age of A = 30 years
    According to question ,
    ∴ age of A + age of D = age of B + age of C
    ⇒ A + D = B + C
    ⇒ 30 + D = B + 40 ⇒ D – B = 10
    ∴ age of B = 35 years and age of D = 45 years